How to Solve Count the Number of Computer Unlocking Permutations Problem
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Count the Number of Computer Unlocking Permutations
You are given an array complexity of length n. There are n locked computers in a room with labels from 0 to n - 1, each with its own unique password. The password of the computer i has a complexity co...
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Understanding the Count the Number of Computer Unlocking Permutations Problem
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Problem Statement
You are given an array complexity of length n. There are n locked computers in a room with labels from 0 to n - 1, each with its own unique password. The password of the computer i has a complexity complexity[i]. The password for the computer labeled 0 is already decrypted and serves as the root. All other computers must be unlocked using it or another previously unlocked computer, following this information: You can decrypt the password for the computer i using the password for computer j, where j is any integer less than i with a lower complexity. (i.e. j < i and complexity[j] < complexity[i]) To decrypt the password for computer i, you must have already unlocked a computer j such that j < i and complexity[j] < complexity[i]. Find the number of permutations of [0, 1, 2, ..., (n - 1)] that represent a valid order in which the computers can be unlocked, starting from computer 0 as the only initially unlocked one. Since the answer may be large, return it modulo 109 + 7. Note that the password for the computer with label 0 is decrypted, and not the computer with the first position in the permutation.
Count the Number of Computer Unlocking Permutations
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Examples
complexity = [1,2,3]2The valid permutations are: [0, 1, 2] Unlock computer 0 first with root password. Unlock computer 1 with password of computer 0 since complexity[0] < complexity[1]. Unlock computer 2 with password of computer 1 since complexity[1] < complexity[2]. [0, 2, 1] Unlock computer 0 first with root password. Unlock computer 2 with password of computer 0 since complexity[0] < complexity[2]. Unlock computer 1 with password of computer 0 since complexity[0] < complexity[1].
complexity = [3,3,3,4,4,4]0There are no possible permutations which can unlock all computers.
Constraints
2 <= complexity.length <= 1051 <= complexity[i] <= 109How Interview Coder Helps with Leetcode Problems
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